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A note on Ramanujan-type integrals
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DOI：10.1080/10652469.2026.2634766.png)
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Abstract
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In this note, we employ elementary methods to investigate new classes of Ramanujan-type integrals involving trigonometric and hyperbolic functions. We establish explicit formulas that express these integrals in terms of special functions, such as the (inverse) trigonometric functions, (alternating) Riemann zeta function, Dirichlet beta function and the Gamma function. Utilizing these formulas, we also directly derive several known results related to Ramanujan-type integrals, thereby providing a unified and simplified approach to their evaluation.
Keywords:
Ramanujan-type integrals
contour integration
Gamma function
(alternating) Riemann zeta function
Dirichlet beta function
Ces & agrave
ro summation
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